Dividing exponents

How to divide exponents.

Dividing exponents with same base

For exponents with the same base, we should subtract the exponents:

a n / a m = a n-m

Example:

26 / 23 = 26-3 = 23 = 2⋅2⋅2 = 8

Dividing exponents with different bases

When the bases are different and the exponents of a and b are the same, we can divide a and b first:

a n / b n = (a / b) n

Example:

63 / 23 = (6/2)3 = 33 = 3⋅3⋅3 = 27

When the bases and the exponents are different we have to calculate each exponent and then divide:

a n / b m

Example:

62 / 33 = 36 / 27 = 1.333

Dividing negative exponents

For exponents with the same base, we can subtract the exponents:

a-n / a-m = a-n-(-m) = am-n

Example:

2-3 / 2-5 = 25-3 = 22 = 2⋅2 = 4

When the bases are different and the exponents of a and b are the same, we can multiply a and b first:

a-n / b-n = (a/b)-n = 1 / (a/b)n = (b/a)n

Example:

3-2 / 4-2 = (4/3)2 = 1.7778

When the bases and the exponents are different we have to calculate each exponent and then divide:

a-n / b-m = bm / an

Example:

3-2 / 4-3 = 43 / 32 = 64 / 9 = 7.111

fractions with exponents

Dividing fractions with exponents with same fraction base:

(a / b)n / (a / b)m = (a / b)n-m

Example:

(4/3)3 / (4/3)2 = (4/3)3-2 = (4/3)1 = 4/3 = 1.333

Dividing fractions with exponents with same exponent:

(a / b)n / (c / d)n = ((a / b)/(c / d))n = ((a⋅d / b⋅c))n

Example:

(4/3)3 / (3/5)3 = ((4/3)/(3/5))3 = ((4⋅5)/(3⋅3))3 = (20/9)3 = 10.97

Dividing fractions with exponents with different bases and exponents:

(a / b) n / (c / d) m

Example:

(4/3)3 / (1/2)2 = 2.37 / 0.25 = 9.481

Dividing fractional exponents

Dividing fractional exponents with same fractional exponent:

a n/m / b n/m = (a / b) n/m

Example:

33/2 / 23/2 = (3/2)3/2 = 1.53/2 = (1.53) = 3.375 = 1.837

Dividing fractional exponents with same base:

a n/m / a k/j = a (n/m)-(k/j)

Example:

23/2 / 24/3 = 2(3/2)-(4/3) = 2(1/6) = 62 = 1.122

Dividing fractional exponents with different exponents and fractions:

a n/m / b k/j

Example:

23/2 / 24/3 = (23) / 3(24) = 2.828 / 2.52 = 1.1222

Dividing variables with exponents

For exponents with the same base, we can subtract the exponents:

xn / xm = xn-m

Example:

x5 / x3 = (x⋅x⋅x⋅x⋅x) / (x⋅x⋅x) = x5-3 = x2


Currently, we have around 1975 calculators, conversion tables and usefull online tools and software features for students, teaching and teachers, designers and simply for everyone.

You can find at this page financial calculators, mortgage calculators, calculators for loans, calculators for auto loan and lease calculators, interest calculators, payment calculators, retirement calculators, amortization calculators, investment calculators, inflation calculators, finance calculators, income tax calculators, compound interest calculators, salary calculator, interest rate calculator, sales tax calculator, fitness & health calculators, bmi calculator, calorie calculators, body fat calculator, bmr calculator, ideal weight calculator, pace calculator, pregnancy calculator, pregnancy conception calculator, due date calculator, math calculators, scientific calculator, fraction calculator, percentage calculators, random number generator, triangle calculator, standard deviation calculator, other calculators, age calculator, date calculator, time calculator, hours calculator, gpa calculator, grade calculator, concrete calculator, subnet calculator, password generator conversion calculator and many other tools and for text editing and formating, downloading videos from Facebok (we built one of the most famous Facebook video downloader online tools). We also provide you online downloanders for YouTube, Linkedin, Instagram, Twitter, Snapchat, TikTok and other social media sites (please note we does not host any videos on its servers. All videos that you download are downloaded from Facebook's, YouTube's, Linkedin's, Instagram's, Twitter's, Snapchat's, TikTok's CDNs. We also specialise on keyboard shortcuts, ALT codes for Mac, Windows and Linux and other usefull hints and tools (how to write emoji online etc.)

There are many very usefull online free tools and we would be happy if you share our page to others or send us any suggestions for other tools which will come on your mind. Also in case you find any of our tools that it does not work properly or need a better translation - please let us know. Our tools will make your life easier or simply help you to do your work or duties faster and in more effective way.

These below are the most commonly used by many users all over the world.

And we are still developing more. Our goal is to become the one-stop, go-to site for people who need to make quick calculations or who need to find quick answer for basic conversions.

Additionally, we believe the internet should be a source of free information. Therefore, all of our tools and services are completely free, with no registration required. We coded and developed each calculator individually and put each one through strict, comprehensive testing. However, please inform us if you notice even the slightest error – your input is extremely valuable to us. While most calculators on Justfreetools.com are designed to be universally applicable for worldwide usage, some are for specific countries only.


Page Id: 1530

This website uses cookies to improve your experience, analyze traffic and display ads. Learn more